Abstract
In this paper, inspired by the Costello’s seminal work [11], we present a general formulation of exact renormalization group (RG) within the Batalin-Vilkovisky (BV) quantization scheme. In the spirit of effective field theory, the BV bracket and Laplacian structure as well as the BV effective action (EA) depend on an effective energy scale. The BV EA at a certain scale satisfies the BV quantum master equation at that scale. The RG flow of the EA is implemented by BV canonical maps intertwining the BV structures at different scales. Infinitesimally, this generates the BV exact renormalization group equation (RGE). We show that BV RG theory can be extended by augmenting the scale parameter space R to its shifted tangent bundle T [1]ℝ. The extra odd direction in scale space allows for a BV RG supersymmetry that constrains the structure of the BV RGE bringing it to Polchinski’s form [6]. We investigate the implications of BV RG supersymmetry in perturbation theory. Finally, we illustrate our findings by constructing free models of BV RG flow and EA exhibiting RG supersymmetry in the degree −1 symplectic framework and studying the perturbation theory thereof. We find in particular that the odd partner of effective action describes perturbatively the deviation of the interacting RG flow from its free counterpart.
Highlights
Analog of the Poisson bracket, and canonical map can in this way be formulated and used while keeping manifest covariance and BRST invariance
In this paper, inspired by the Costello’s seminal work [11], we present a general formulation of exact renormalization group (RG) within the Batalin-Vilkovisky (BV) quantization scheme
We investigate the implications of BV RG supersymmetry in perturbation theory
Summary
The effectiveness of the BV RGE as a computational scheme and analysis method depends on the form of the RG flow, which is a basic input datum of the RGE itself. St obeys an RGE of the form dSt dt φtSt. in which the first and second term of the right hand side can be identified with the familiar “classical” and “quantum” contributions to the RG flow. In analogy to basic case, its RG flow is governed by a group φtθ,sζ of canonical maps relating the BV bracket and Laplacian at any extended scale s, ζ to those at another scale t, θ according to the law Stθ = φtθ,sζ ∗Ssζ + rφtθ,sζ. Where the last two terms in the right hand side are “seed” terms In this way, we obtain a version of the BV RGE of the distinctive form of Polchinski’s [6] by purely algebraic and geometric means. In a more mathematical oriented paper [23], we shall reformulate the results obtained here in the framework of the abstract theory of BV algebras and manifolds
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
